Ma kēia paʻi ʻana, e noʻonoʻo mākou i kekahi o nā manaʻo nui o ka geometry Euclidean - ʻo Stewart's theorem, i loaʻa ia inoa no ka hanohano o ka mea makemakika Pelekane ʻo M. Stewart, nāna i hōʻoia. E hoʻopili kikoʻī mākou i kahi laʻana o ka hoʻoponopono ʻana i ka pilikia e hoʻohui i nā mea i hōʻike ʻia.
ʻO ka ʻōlelo o ka theorem
huinakolu Dan ABC. Ma kona aoao AC helu ʻia D, i pili i luna B. ʻAe mākou i kēia notation:
- AB = a
- BC = b
- BD = p
- AD = x
- DC = a
No kēia huinakolu, ʻoiaʻiʻo ka kaulike:
Ka hoohana ana i ka manao
Mai ke kumukānāwai a Stewart, hiki ke loaʻa i nā kumu no ka huli ʻana i nā waena a me nā ʻāpana ʻāpana o kahi huinakolu:
1. ʻO ka lōʻihi o ka mahele ʻāpana
e lc ʻo ka mahele ʻelua i huki ʻia ma ka ʻaoʻao c, i maheleia i mau apana x и y. E lawe kakou i na aoao elua o ka huinakolu a и b… I kēia hihia:
2. Loihi waena
e mc ua huli ka waena ma ka ʻaoʻao c. E hoailona kakou i na aoao elua o ka huinakolu a и b… A laila:
Laʻana o kahi pilikia
Hāʻawi ʻia ka Triangle ʻAmelisa. Ma ka ʻaoʻao AC like me 9 knm, helu ʻia D, ka mea e mahele ana i ka aoao AD pālua ka lōʻihi DC. ʻO ka lōʻihi o ka māhele e hoʻopili ana i ka vertex B a kuhikuhi D, he 5 knm. I kēia hihia, ka triangle i hana ʻia US he isosceles. E imi i na aoao i koe o ka huinakolu ABC.
pāʻoihana
E hōʻike i nā kūlana o ka pilikia ma ke ʻano o kahi kiʻi.
AC = AD + DC = 9 knm. AD hou DC ʻelua, ʻo ia hoʻi AD = 2DC.
ʻO ke kumu iho, ʻo 2DC + DC = 3DC u9d XNUMX kenimika. No laila, DC = 3 knm, AD = 6 knm.
No ka huinakolu US – isosceles, a me ka aoao AD he 6 knm, no laila ua like lākou AB и BDIe AB = 5 knm.
ʻO ka loaʻa wale nō ia BC, e loaʻa ana i ke kumu hoʻohālike mai kā Stewart theorem:
Hoʻololi mākou i nā waiwai i ʻike ʻia i kēia ʻōlelo:
I keia ala, BC = √52 ≈ 7,21 knm.